Geometric flows have many applications in physics and geometry. The mean curvature flow occurs in the description of the interface evolution in certain physical

This work gives a coherent introduction to isoperimetric inequalities in Riemannian manifolds, featuring many of the results obtained during the last 25 years a

In this thesis, we give a lower bound on the areas of small geodesic balls in an immersed hypersurface M contained in a Riemannian manifold N. This lower bound